Data transmission using optical fibers involves the propagation of pulses of light through the fibers. A light pulse generated at a specific frequency ω actually consists of a spectrum, i.e., a distribution of energy over a band of frequencies, with the peak of the spectrum occurring at frequency ω. The frequency at which the peak of a pulse occurs is known as the central frequency of the pulse. FIG. 1 shows a light pulse generated at frequency ω with a peak intensity I. The bandwidth of the pulse is defined as the range of frequencies wherein the frequency components of the pulse have a specified fraction of intensity of the pulse peak. Typically, the pulse bandwidth is defined as the full width at half maximum intensity, or “FWHM”, which means the range of frequencies wherein the frequency components of the pulse have half the intensity of the pulse peak.
Another characteristic of a pulse is its width. Pulse width refers to the time duration of a pulse. Pulse width and pulse bandwidth are inversely related such that increasing a pulse's width decreases its bandwidth and vice versa.
In a binary digital communication system, two discrete states are used for communication, i.e., ones and zeros. In a binary system, a single discrete state represents a unit of information known as a bit. Thus a binary data stream consists of a stream of time slots, or “bit periods”, where each bit period contains either a one or a zero. In an optical system, the presence or absence of a pulse within a bit period signifies a discrete state. For example, the presence of a pulse could signify a one for that period whereas the absence of a pulse would signify a zero. Thus, a stream of pulses, known as a pulse train, is used in an optical system to represent a binary data stream.
As light pulses travel through a fiber optic transmission line, they may be distorted in a variety of ways which affect their ability to represent binary digital data. Thus various techniques and transmission line designs exist which attempt to combat various types of distortion.
One type of distortion affecting light pulses is dispersion. Dispersion causes a differential phase shift in the frequency components of a pulse which causes these frequency components to become “chirped”, i.e., out of phase relative to each other. As the frequency components of the pulse become chirped, the pulse spreads out in time. Thus dispersion causes the width of a pulse to broaden as the pulse propagates down the fiber. It should be noted here that a pulse of a given bandwidth has its narrowest pulse width when the frequency components of the pulse are in phase. In this condition, the pulse is said to be “unchirped”.
If the pulse widths become too large, adjacent pulses begin to overlap in time and to interact with each other. This interaction is another type of distortion, in which the pulses tend to be moved from their proper positions in time and so cause error. If pulse widths become still larger, pulses in successive bit periods will overlap, making it difficult to distinguish and detect the data represented by those pulses.
The amount of dispersion affecting pulses is dependent on the properties of the optical fiber. An optical fiber's dispersion constant, or “D”, describes the amount of dispersive effect that fiber has on pulses travelling through it.
One technique for combating the pulse width broadening effect of dispersion is to transmit data using a special type of pulse, known as a soliton, which is resistant to dispersion. The soliton resists dispersion by taking advantage of another type of distortion, known as self-phase modulation, or “SPM”, which counters the pulse width broadening of dispersion.
Like dispersion, SPM also causes a differential phase shift across a light pulse. However, the differential phase shift caused by SPM does not broaden the pulse in time. Rather, the SPM differential phase shift causes new frequency components to be added to a pulse as it travels through an optical fiber. The addition of new frequency components to the pulse increases the pulse's bandwidth.
The amount of SPM affecting a pulse is determined by the pulse's intensity. Thus, the stronger the pulse's intensity, the greater the effect of SPM, and the more the pulse's bandwidth will be increased.
In a soliton, dispersion and SPM cancel each other's effects because the differential phase shift across the pulse caused by dispersion and the differential phase shift across the pulse caused by SPM sum to a constant phase shift across the pulse. This constant phase shift across the pulse does not affect either the pulse's width or bandwidth. Thus, a soliton's pulse width and bandwidth remains stable as it propagates through an optical fiber transmission line.
Another type of distortion is known as timing jitter. The pulses in a particular pulse train ideally all have the same central frequency. However, optical amplifiers along the transmission line create spontaneous emission noise which causes small, random alterations in the central frequencies of the pulses. The cumulative dispersion encountered by pulses as they travel down the transmission line converts these alterations in central frequency into differences in pulse arrival times, i.e., the time at which a pulse arrives at a particular location in the transmission line such as the receiver. If the cumulative dispersion encountered by pulses is large, the corresponding large differences in arrival times can result in the pulses being received at the incorrect time slot or bit period. This leads to errors in decoding the information represented by the pulses.
Other types of distortion are encountered in optical systems employing wavelength division multiplexing or “WDM”. WDM refers to the use of different frequencies or wavelengths as distinct communication channels within a single optical fiber.
Communication channel, or simply channel, refers to the means through which a data communication stream is sent. Communication systems may employ multiple channels so as to transmit multiple data communication streams simultaneously. In optical communications, different channels may be created using different frequencies or wavelengths. Thus the different channels can be said to be divided, i.e., separated, by frequency or wavelength.
Furthermore, when multiple channels are placed in a single physical path, they are said to be multiplexed. Thus, WDM refers to the situation where multiple frequency or wavelength channels exist within a single optical fiber. FIG. 2 shows three channels of a WDM system at frequencies ω1, ω2 , and ω3 . The frequency interval Δω between frequency channels is known as the channel spacing of the system.
As can be seen from FIG. 2, the spectral density of a WDM system, i.e., the number of frequency channels which can be placed within a given frequency range, is limited by the bandwidth of the pulses if we are to avoid significant overlapping between the spectra of adjacent channels. Consequently, narrower pulse bandwidths allows for more frequency channels to be used in a given frequency range.
In a transmission system employing WDM, two types of distortion, known as four-wave mixing and cross-phase modulation, result from interaction between pulses as pulses of adjacent frequency channels pass through each other. In general, these effects have the potential to bring about a significant exchange of energy and momentum between the pulses which creates timing jitter and amplitude jitter, the latter referring to fluctuations in the intensity of the pulses.
The timing jitter resulting from cumulative dispersion and the effects of four-wave mixing and cross-phase modulation can be reduced through the use of dispersion management. Dispersion management is a technique for designing transmission lines. A dispersion managed transmission line is designed with periodic sections, i.e., identical sections which are repeated one after another along the transmission line. Each section is made up of two or more different types of fiber having alternating positive and negative values of D. The sequence of D values along such a transmission line is known as a D map and each section of the transmission line is represented by a single D map period.
With dispersion management, the different types of fiber and the lengths of those fibers used in each D map period are chosen such that (1) the absolute value of the instantaneous D at any point along the D map period, known as |Dloc|, is high, i.e., 3 ps/(nm-km) or higher, (2) while at the same time the path average dispersion, or “ D”, for the D map period is at or near zero, i.e., 0.5 ps/(nm-km) or lower. Path average dispersion is defined as                                           D            _                    =                                    1              L                        ⁢                                          ∫                0                L                            ⁢                                                D                  ⁢                                      (                    z                    )                                                  ⁢                                                                   ⁢                                  ⅆ                  z                                                                    ,                            (        1        )            where D(z) is the instantaneous value of D at any point along the D map period and L is the length of the D map period.
Qualitatively, the concept of dispersion management can be represented by a D map having two segments of fiber, for example one segment of 20 km and having D of +11 ps/(nm-km) and another segment of 20 km and having D of −10 ps/(nm-km). The |Dloc| at any point along the D map period is high, i.e., approximately 11 ps/(nm-km) or 10 ps/(nm-km), while D, which can be approximately calculated as [(+11)(20 km)+(−10)(20 km)] 1/40=0.5 ps/(nm-km), is low. However, this qualitative example assumes that D remains perfectly constant over the entire length of a fiber. In reality, D wanders somewhat from the expected value all along the length of the fiber. Therefore, D is most accurately defined by equation (1) above.
In a dispersion managed transmission line, the high |Dloc| reduces the effects of four-wave mixing and makes the effects of cross-phase modulation more manageable. Also, since D is at or near zero, the cumulative dispersion encountered by pulses is very low and thus timing jitter is kept to a minimum.
FIG. 3 shows the D map period of a conventional dispersion managed soliton transmission line. This prior art D map period contains two sections of fiber, the first having a positive D, or “+D”, and a long length than the second section which has a very large negative D, or “−D”, and a short length. Also, the prior art D map period contains several optical amplifiers 10. The distance between optical amplifiers is known as the amplifier period. Thus, the prior art D map period is several amplifier periods long.
Conventional dispersion managed soliton transmission lines having D maps similar to that shown in FIG. 3 are deficient in several ways. In such a transmission line, only pulses of short widths have significant energy at or near D=0 while pulses of longer widths have zero or minimal energy at or near D=0. Pulses propagating through an optical fiber transmission line must have a minimum threshold of path average pulse energy if the signal-to-noise ratio is to be high enough to achieve error free transmission over very long, e.g., transoceanic, distances. Thus, in transmission lines having this prior art D map, only solitons with short pulse widths (and large bandwidths) have this adequate level of path average pulse energy at or near D=0 while solitons with long pulse widths (and narrow bandwidths) do not. In a WDM system, large pulse bandwidths restrict the system to fewer frequency channels for a given frequency range. This results in a low spectral efficiency for a transmission line having this prior art D map. Spectral efficiency, which is defined as the bit-rate/channel separation, is a measure of the communication efficiency of a WDM system.
Furthermore, at or near D=0, the path average pulse energy of solitons in this transmission line depends critically on both D and the pulse width τ. This critical dependence makes this transmission line less practical for use since in real world systems D and generated pulse widths can vary.
Also, a prior art transmission line having a D map similar to FIG. 3 is deficient because the D map period is not the same as the amplifier period. Creating transmission lines where the D map period is multiple amplifier periods long is often disadvantageous. For one thing, the long period tends to produce too great pulse breathing, with the result of excessive adjacent pulse interaction. However, if these prior art D maps are altered so that the amplifier period is made to be the same as the D map period, the pulse breathing in the +D section of the D map period becomes highly asymmetric. This in turn also results in excessive pulse interaction.
Pulse breathing refers to the contraction and expansion of a pulse's width as it propagates through an optical fiber. As stated previously, dispersion causes the soliton pulse width to increase and SPM tends to counteract this effect in +D fiber. Since SPM is dependent on the intensity of the pulse, the effects of SPM are strongest at the beginning of the +D section, where the pulse has just been energized by the optical amplifier, and will gradually decrease and be weakest at the end of the +D section since the pulse experiences loss as it propagates through the fiber. Consequently the pulse broadening effect of dispersion is more strongly compensated by SPM at the beginning of the +D section and less compensated at the end of the +D section. This uneven compensation results in asymmetric pulse breathing.
Where pulse breathing is symmetrical the pulse width will vary from maxima which are nearly equal. However, for the same total dispersion in the map, where the pulse breathing is asymmetrical, the pulse width will vary to a maximum width which considerably exceeds the maxima of the symmetrical situation. Thus, the condition of symmetry facilitates keeping the pulse breathing within the limits required for negligible pulse interaction.